6. Given large random samples from two binomial populations, show that the null hypothesis $\theta_{1}=\theta_{2}$ can be tested on the basis of the statistic $$ z=\frac{\frac{x_{1}}{n_{1}}- \frac{x_{2}}{n_{2}}}{\sqrt{\hat{\theta) (1-\hat{\theta})\left(\frac{1} {n_{1}}+\frac{1}{n_{2}} ight)}} $$ SP.DL.2011